MORE REVISION 20040201
This sheet should be done entirely without calculators. The idea is to help you remember some conversions, remember some rules and to apply some skills.
1The number of grammes in a pound is ____________
2A mile is _____________________ metres to 4 sig. fig.(no, not seven)
3There are __________ litres in a gallon (probably 3 sig.fig.)
4An acre, __________ sq yds, is a c__________ by a f_______________
5 (-23) 2 = ___________ 24 2 = ______ -(25) 2 = ___________
626 2 - 24 2 = 50 x ____ = _____ 29 2 - 21 2 = 8 x ______ =
7The difference of two squares is …………………… times ………………………
( x2 - y 2) = ( ) ( )
So, without knowing or needing either square, we can work out
8562 - 442=
9762 - 242 =
101442 - 562 =
and when we do know some squares (up to 30 squared and all ending in 5), then the rule works in reverse, so we can do
11 (29 + 7) (29 - 7)=
12 106 x 94 =
13 88 x 72 =
If you have any time left: treat this as a logical problem, or recognise matrix methods, or both:
14 TRY to fill in the gaps here: 12 x + 7 y = 19 so ( 12 7 )( x ) = ( 19)
3 x + 2 y = -17 ( )( y ) ( )
PREMULTIPLY both ( 2 -7 ) ( 12 7 )( x ) =( 2 ) ( 19)
sides by the same thing ( ) ( 3 )( y ) ( ) ( )
Do matrix multiplication ( 0 ) ( x ) = () = ( )
(I’ve given you enough) ( 0 ) ( y ) ( ) ( )
DIVIDE both sides by ( x ) = ( ) a pair of
the three ( y ) ( ) fractions